How do I stop my chain distorting along a curve?
The origin of both objects (chain and curve) matters for the curve modifier.

To correct the issue:


Place the 3D cursor on the first vertex of the curve, then come back in object mode and transform the curve origin to the 3D cursor.
And move the chain to that origin (considering the chain origin is ok, relatively to the chain itself)




Some information or tips:

Here we start with a simple position where all objects are oriented along the X axis and the curve modifier is set along X too (the modifier's result is not shown below).



Now we activate the modifier and grab the chain's origin near the curve origin:



We notice that:


The more the chain is near the curve, the less it is stretched
When both origins are at the same location, the chain begins at the first curve's control point


If we rotate, move, or change the chain in edit mode:



If we rotate, move, or change the chain in edit mode:



And if we change the chain's control points:



So aligning the chain and the curve:


Set both origins at the same location
Set the modifier's axis along the chain axis
The chain will be curved starting at the first control point of the curve and starting from its own origin (and the result depends on the position of its inner geometry relative to its origin)